Lecture 8 Flashcards
In finance, risk neutral=
EV maximiser
How can risk averseness partly explain the st Petersburg paradox?
The CE prospect of the game whose EV was infinite, was below £5. One reason is that people are normally risk averse - Bernoulli’s solution using EU instead of works since EU captures attitudes towards risk
What is meant by the following term:
α(p)β EU(α(p)β)<u></u>
x, the EV(α(p)β), will be preferred to the prospect α(p)β IF AND ONLY IF the utility of x (=EU(x)) is greater than the EU of the prospect α(p)β
See diagram and learn it
Notes
See 2nd example and check understand it
Now
Good way to see risk averseness?
A person will be risk averse if the expected utility of the prospect is less than the expected utility of the EV
Explain risk aversion in terms of shape of utility function, u(EV) vs EU, EV vs CE and premium?
Concave utility
EV>CE tf u(EV)>EU
Tf positive risk premium
Explain risk neutrality in terms of shape of utility function, u(EV) vs EU, EV vs CE and premium?
Linear utility
EV=CE tf u(EV)=EU
Tf zero risk premium
Explain risk seeking in terms of shape of utility function, u(EV) vs EU, EV vs CE and premium?
Convex utility
EV
See example on insurance in notes
Now
How (if you can) should you represent the decision for the consumer?
ITO final wealth level
Why do insurance companies make a profit?
Because of consumer’s risk aversion
What is the risk premium? (2)
Risk premium=EV-CE
=exact profit margins for insurance companies
Explain what a mean-preserving spread is and what it shows?
A mean-preserving spread replaces the outcome x(j) and it’s probability p(j) by 2 outcomes M, m, with probabilities qp(j) and (1-q)p(j) such that the expectation of the prospect is unaltered
It shows risk aversion attitudes (see diagram in notes)
